Xii Inverse Trigo Assignment

  • May 2020
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ASSIGNMENT CLASS XII INVERSE TRIGONOMETRY Q1. Find the principle value of the following: (a) sin 1 (

1 ) 2

 

(f) sin 1  sin

 3   2 

(b) cos 1  

(d) sec 1 (2)

(c) tan 1 ( 3)

3  5  2  1  1   (g) cos  cos  (h) tan  tan  4  4  3   

 

(i) cos 1  cos

(e) cos ec 1 (  2)

8  5  1   (j) tan  tan  7  6  

Q2. Evaluate the following:



 3     5     8  (d) tan  cos 1     17   



 4     5    1   (e) tan  2 tan 1     5 4  

(a) cos  sin 1 

(b) cos ec  cos 1 



 3   4     3   (f) sin  2cos 1    5   (c) cos  tan 1   

Q3. Prove the following:

1 1   tan 1  3 7 4 5 2 1  1 1 (c) 2 tan 1  sec 1     2 tan  5 8 4  7   (e) 2 cot 1 5  cot 1 7  2 cot 1 8  4 5 3 63 (g) sin 1  cos 1  tan 1 13 5 16  1   1  3 (i) tan 1 1  cos 1    sin 1     2   2  4 (a) 2 tan 1

(b) sin 1

4 5 16   sin 1  sin 1  5 13 65 2

(d) tan 1

1 1 3 1   tan 1  tan 1  tan 1  2 3 5 4 4

3 17   tan 1  5 31 4 4 3 27 (h) cos 1  tan 1  tan 1 5 5 11 2 2  1  x  1  1  x   (j) sin  tan 1  1   cos  2   2x   1  x   (f) 2sin 1

Q4. Write the following in the simplest form:

 sin x    1  cos x 

(a) tan 1 

ax ax

(d) tan 1

 1  x2  1  x2 (b) tan 1   1  x2  1  x2 



   

 cos 2 x    1  sin 2 x 

(c) tan 1 



(f)

(b) tan 1  x  1  tan 1  x  1  tan 1

6 17

 

(e) cos tan 1 sin cot 1 x

cot 1



1  x2  x



Q5. Solve the following equations:

1 x  1 1   tan x 1 x  2

(a) tan 1 

 3  (e) sin 1 x  cos 1 x  6 (c) sin 1 x  sin 1 2 x 

(d) cos 1 x  sin 1

x   2 6

(f) 4sin 1 x  cos 1 x  

ANSWERS

 5  2   3  6  (b) (c) (d) (e) (f) (g) (h) (i) (j) 4 6 3 3 4 4 4 3 7 6 4 5 4 15 7 24   1  1 x 2. (a) (b) (c) (d) (e) (f) 4.(a) (b)  cos 1 x 2 (c)  x (d) cos 1 5 3 5 17 17 25 2 4 2 4 2 a 2 1 1 3 3 x 1  1 1 1 1 e) (f)  tan x 5.(a) (b) (c) (d)  1 (e) (f) 2 x 2 4 2 3 2 7 2 2 3 1.(a)

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